We are glad that Sharer et al. (this issue) have dropped their original claim that the INAA data demonstrate multidirectional movement of Early Formative pottery. Beyond this, however, they offer nothing that might enhance understanding of Early Formative ceramic circulation or inspire new insights into Early Formative cultural evolution in Mesoamerica. Instead, their response contains fresh distortions, replications of mistakes made in their PNAS articles, and lengthy passages that are irrelevant to the issues raised by Neff et al. (this issue). We correct and recorrect their latest distortions and misunderstandings here. Besides showing why their discussion of ceramic sourcing repeatedly misses the mark, we also correct a number of erroneous assertions about the archaeology of Olmec San Lorenzo. New evidence deepens understanding of Early Formative Mesoamerica but requires that some researchers discard cherished beliefs.

A recent study of Early Formative Mesoamerican pottery by instrumental neutron activation analysis (INAA) yielded surprising results that prompted two critiques in the Proceedings of the National Academy of Sciences. The INAA study indicated that the Olmec center of San Lorenzo was a major exporter of carved-incised and white pottery and that little if any pottery made elsewhere was consumed at San Lorenzo. The critiques purport to "overturn" the INAA study and demonstrate a more balanced exchange of pottery among Early Formative centers. However, the critiques rely on a series of mistaken claims and misunderstandings that are addressed here. New petrographic data on a small sample of Early Formative pottery (Stoltman et al. 2005) are potentially useful, but they do not overturn INAA of nearly 1000 pottery samples and hundreds of raw material samples.